Question 1158139
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<pre>

Let x (kilometres per hour) be the average speed for the first 40 km.

Then the remaining 90-40 = 50 milometers his average speed was (x+20) kilometres per hour.


The traveling time for the first 40 kilometres was  {{{40/x}}}  hours.

The traveling time for the remaining 50 kilometres was  {{{50/(x+20)}}}  hours.


The total time was 1 hour

    {{{40/x}}} + {{{50/(x+20)}}} = 1  hour.


It is your "time" equation.


To solve it, multiply both sides by x*(x+20). you will get then

    40*(x+20) + 50x = x*(x+20).


Simplify and solve

    40x + 800 + 50x = x^2 + 20x

    x^2 - 70x - 800 = 0

    x = {{{(70 +- sqrt(70^2 + 4*1*800))/2}}} = {{{(70 +- sqrt(8100))/2}}} = {{{70 +- 90)/2}}}.


Of the two roots, only positive value x = {{{(70+90)/2}}} = 80 is the solution to the problem.


<U>ANSWER</U>.  The average speed for the first 40 km was 80 km/h.
</pre>

Solved.


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Using &nbsp;&nbsp;"time" &nbsp;equation is a &nbsp;STANDARD &nbsp;method of solving such problems.

From this lesson, &nbsp;learn on how to write, &nbsp;how to use and how to solve a &nbsp;"time" &nbsp;equation.


To see many other similar solved problems, &nbsp;look into the lessons

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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Time-equation-HOW-TO-write-it-and-how-to-solve-it.lesson>Time equation: HOW TO use, HOW TO write and HOW TO solve it</A> 

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